Apparatus for breaking off the edge strip of a glass sheet scratched in a blank according to some predetermined contour is known in the prior art. Representative of the prior art is U.S. Pat. No. 4,371,103 to Selmens. According to the patent, pressure pins which are placed apart at short distances from one another are lowered onto a glass sheet disposed therebelow. This action is carried out as the glass sheet resides on a flexible elastic support in a manner that a greater surface pressure is brought to bear on the edge strips outside of the contour line than on the glass sheet inside the contour line. Quite obviously the pressure forces exerted by the pressure pins must act on different points, and the locations of action will be different for glass sheets of different shape and size. Normally, the pressure pins are arranged in a known arrangement in the same housings on a common carrier plate and for purposes of changing the points of the action of the pressure forces exerted by the pressure pins, the housings are mounted in slidable fashion on a common carrier plate. To adjust the points of action of the pressure pins for operating on glass sheets of different size and shape it is necessary to detach the housings carrying the groups of pressure pins from the carrier plate and, then, refasten the housings on the carrier plate at another location. This changeover operation of the apparatus to accommodate another glass sheet shape or another glass sheet size requires an interruption in production. Because the changeover operation requires a certain amount of time, and is carried out by hand, there is a loss of production output and a loss financially.